On the Breaking of Progressive Waves in Shallow Water

Singularities at the crest offer longstanding difficulties in understanding the breaking of water waves. In this paper, one of systems, representing periodic and solitary progressive waves and the breaking in shallow water, is discussed and it is derived from perturbation for the Hamiltonian function of Korteweg & de Vries equation. The Lagrangian function of the variational principle and the universal unfolding in functional spaces are applied in this procedure. From the analysis waves show the singularities at the crest in terms of unknown perturbation parameter. This perturbed terms are similar to those in the second order approximation for the nonlinear long water wave theory. This system, then, is concidered one of simple models for the breaking of waves